Question

Find X and Y in each of the following, where DE || BC .
Give the accurate answer stepwise. ​

Answer 1

Answer:

x = 55

y = 55

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Step-by-step explanation:

sum of all the angles in a triangle = 180

55 degrees and y are alternate angles so y = 55

y and x are equal so x = 55

Answer 2

Answer + Step-by-step explanation:

IN TRIANGLE ABC

∠ B.A.C = ∠ y              ( ANGLES OPP. TO EQUAL SIDES ARE EQUAL )

∠x = ∠E.A.C                 ( ALT. INT. ANGLES ,DE║BC)

∠DAB + ∠B.A.C + ∠E.A.C = 180°         ( STRAIGHT LINE )

55° + ∠y + ∠x = 180°

∠y + ∠x = 180° - 55°

y + x = 125°

IN TRIANGLE ABC

∠Y + ∠Y + ∠X = 180°             ( ANGLE SUM PROPERTY )

∠Y + 125° = 180°                      ( ∵ Y + X = 125° )

∠Y = 180° - 125°

∠Y = 55°

SUBSTITUTING IN ANGLE SUM PROPERTY

∠Y + ∠Y + ∠X = 180°

55° + 55° + ∠X = 180°

110° + ∠X = 180°

∠X = 180° - 110°

∠X = 70°

∴ X = 70° ,  Y = 55°